Mathematica subtracting matrices with missing value

Question

In Mathematica, I have a matrix 'a' with missing values and I have a matrix 'b' with same dimension as 'a'. I would like to calculate a-b but if the value is missing, which I denote by 'NA', I would like it to remain as 'NA'. Could you please help me with this? Please note that 'a' is of the dimension 1millionX300.

Thanks!

Answer 1

One approach would be to use a replacement rule on the result, something like this;

In[1]  {1, na, 3, na, 5} - {1, 2, 3, 4, 5}
Out[1] {0, -2 + na, 0, -4 + na, 0}

In[2]  {1, na, 3, na, 5} - {1, 2, 3, 4, 5}/. x_ + na -> na
Out[2] {0, na, 0, na, 0}

Another approach would be to define an UpValue for na such that addition (and subtraction) involving it would always result in na; like this:

In[3] na /: Plus[___, na, ___] := na

UpValues would be the way to go if you are going to do the operation more than once, replacement rules for a one-off.

Answer 2

You could use Indeterminate for this, since it already has the behavior your looking for:

In[2]:= {1, na, 3, na, 5} - {1, 2, 3, 4, 5} /. na -> Indeterminate /. Indeterminate -> na

Out[2]= {0, na, 0, na, 0}

Personally, I'd just use Indeterminate to start with, instead of NA.